Identifying Essential Network Properties for Disease Spread Peter J. Mucha, Associate Professor, Department of Mathematics, Institute for Advanced Materials, Nanoscience and Technology, & Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina at Chapel Hill Project Summary (Abstract) Interdisciplinarily rooted across mathematical graph theory, statistics, the social sciences, statistical physics, computer science, and applied mathematics, network analysis holds the potential to make critical insights about the spread of disease in a population, across a variety of mechanisms of biological transmission and behavioral influence. However, to realistically influence future prediction and behavioral intervention, the results of such analysis must not rely on complete and perfect information about the entire underlying network of contagion. Instead, reduced-order mod els of disease spread within the population will continue to be employed; but those models will be improved by additional use of more limited network information, and by an improved understanding about which essential network features influence the predictions and accuracy of models. This proposed research program leverages and combines recent advances in two areas of net- work analysis-approximate models of network-coupled dynamics and new community detection technologies-with the specific aim of generating, exploring, and cataloguing a family of comparisons between network-level simulations and reduced-order models of disease spread. Supporting activities will include (1) development of community-aware sub compartmented models which generalize existing network-aware systems, (2) algorithmic improvement of the new multislice network community detection method, and (3) additional theoretical developments in community detection specifically targeted to support the specific aim of improved modeling of disease spread. The relevance to public health is in the targeted application to improved mathematical modeling of the spread of both biological diseases and social contagions, emphasizing the identification of the essential network structures necessary for accurate modeling. By identifying the essential properties of the underlying networks paired with model equation systems, the results of this study will provide fundamental insight about which network properties must be accurately sampled to understand the disease dynamics in that population, with future implications for population-level modeling and intervention across a wide variety of diseases.